(a)

#### To determine

Whether the series ∑an convergent or divergent.

#### Answer

The comparison test fails.

#### Explanation

**Given:**

The series ∑bn is convergent.

**Result used:** *Comparison Test*

“Suppose that ∑an and ∑bn are the series with positive terms,

(1) If ∑bn is convergent and an≤bn for all n, then ∑an is also convergent.

(2) If ∑bn is divergent and an≥bn for all n, then ∑an is also divergent.”

Since an>bn for all n, ∑an>∑bn.

The series ∑bn is convergent and by using the Result stated above, it can be concluded that the *Comparison Test* fails.

(b)

#### To determine

Whether the series ∑an convergent or divergent.

#### Answer

The series

∑an is convergent.

#### Explanation

**Result used:** Comparison test

“Suppose that ∑an and ∑bn are the series with positive terms,

(1) If ∑bn is convergent and an≤bn for all n, then ∑an is also convergent.

(2) If ∑bn is divergent and an≥bn for all n, then ∑an is also divergent.”

**Given:**

The series ∑bn is convergent.

Since an<bn for all, ∑an<∑bn.

The series ∑bn is convergent and using the result stated above, it can be concluded that the series ∑an is convergent.